Cycles with almost linearly many chords

Chen, Erdős, and Staton asked in 1996 how many edges are required in an n-vertex graph to guarantee a cycle with as many chords as vertices. The best current bound, due to Draganić, Methuku, Munhá Correia, and Sudakov shows that average degree (log n)⁸ already suffices.
In this talk, I will show that constant average degree is enough to guarantee a cycle on $\mathcal{l}$ vertices with at least Ω($\frac{\mathcal{l}}{{\log }^C\left(\mathcal{l}\right)}$) chords answering a question of Dvořák, Martins, Thomassé, and Trotignon asking whether constant-degree graphs must contain cycles whose chord counts grow with their length. This is joint work with Nemanja Draganić.

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There will be coffee and cake after the seminar in the common room